连续广义时滞系统L-K泛函  

L-K functional for continuous singular time-delay systems

作　　者：孙欣[1] 于姗姗 SUN Xin;YU Shanshan(College of Mathematics and Systems Science.Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]沈阳师范大学数学与系统科学学院

出　　处：《沈阳师范大学学报（自然科学版）》2019年第5期395-400,共6页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(61374043);辽宁省教育厅高等学校基本科研项目(LFW201711)

摘　　要：连续广义时滞系统容许性的研究,通过构造具有一定结构的Lyapunov-Krasovskii泛函(简称L-K泛函),对泛函求导,利用一些积分不等式处理泛函求导后的某些积分项,得到以线性矩阵不等式(简称LMI)给出的容许性条件。综合已有的相关研究成果,一方面总结归纳了L-K泛函形式:双重积分型、多重积分型、增广型以及松弛型;另一方面列举比较了几种处理L-K泛函求导后产生积分项常用的积分不等式:Jensen积分不等式、Wirtinger积分不等式、辅助函数积分不等式以及Bessel-Legendre积分不等式(简称B-L积分不等式)。运用这些积分不等式的目的是以LMI的形式给出连续广义时滞系统容许性条件,利于Matlab求解。并且,对这些积分不等式的放缩程度进行比较,因为这直接关系到连续广义时滞系统容许性条件的保守性。Generally,the admissibility condition of continuous singular time-delay systems is gained by some steps.Firstly,the appropriate Lyapunov-Krasovskii functional(L-K functional)is constructed.Then,derivation on the L-K function produces some of integral terms which will be dealt with some integral inequalities.Finally,the admissibility condition is obtained in the form of linear matrix inequality(LMI).An overview of the relevant results of continuous singular time-delay systems is given.For one thing,the forms of L-K functional in the literature are summarized and exampled,which include double integral forms,multiple integral form,augmented dimension form and relaxed form.For another thing,some integral inequalities which are used to deal with the integral terms produced by derivation on the L-K function are exampled and compared.The integral inequalities include the Jensen integral inequality,Wirtinger integral inequality,auxiliary function integral inequality and Bessel-Legendre integral inequality(B-L integral inequality).The aim of using the integral inequalities is to obtain admissibility condition of continuous singular time-delay systems in the form of LMI,which is feasible to obtain solution via Matlab.Simultaneously,the extension degree which decides the conservatism of admissibility condition are compared among the integral inequalities.

关 键 词：连续广义时滞系统 Lyapunov-Krasovskii泛函(L-K泛函) 容许性条件 积分不等式 

分 类 号：O231[理学—运筹学与控制论]